diff --git a/transport/http2/server.go b/transport/http2/server.go
index 1ca5651..ea0493a 100644
--- a/transport/http2/server.go
+++ b/transport/http2/server.go
@@ -51,6 +51,7 @@ type Server struct {
 	closing        bool
 	cancel         context.CancelFunc
 	conns          map[net.Conn]struct{}
+	protocolConns  map[net.Conn]struct{}
 	connSlots      chan struct{}
 	requestSlots   chan struct{}
 	accepted       atomic.Uint64
@@ -204,6 +205,9 @@ func (s *Server) Serve(ctx context.Context, listener net.Listener) error {
 	if s.conns == nil {
 		s.conns = make(map[net.Conn]struct{})
 	}
+	if s.protocolConns == nil {
+		s.protocolConns = make(map[net.Conn]struct{})
+	}
 	if s.MaxConnections > 0 {
 		s.connSlots = make(chan struct{}, s.MaxConnections)
 	} else {
@@ -330,6 +334,7 @@ func (s *Server) serveConn(ctx context.Context, protocolServer *xhttp2.Server, b
 	defer func() {
 		s.mu.Lock()
 		delete(s.conns, conn)
+		delete(s.protocolConns, conn)
 		s.activeConns.Add(-1)
 		s.mu.Unlock()
 		if s.connSlots != nil {
@@ -344,6 +349,13 @@ func (s *Server) serveConn(ctx context.Context, protocolServer *xhttp2.Server, b
 		}
 		_ = conn.SetDeadline(time.Time{})
 	}
+	s.mu.Lock()
+	if s.closing {
+		s.mu.Unlock()
+		return
+	}
+	s.protocolConns[conn] = struct{}{}
+	s.mu.Unlock()
 	protocolServer.ServeConn(conn, &xhttp2.ServeConnOpts{
 		Context: ctx, Handler: handler, BaseConfig: baseConfig,
 	})
@@ -386,6 +398,7 @@ func (s *Server) Shutdown(ctx context.Context) error {
 	for conn := range s.conns {
 		connections = append(connections, conn)
 	}
+	protocolConnectionCount := len(s.protocolConns)
 	s.mu.Unlock()
 	if listener != nil {
 		_ = listener.Close()
@@ -394,7 +407,7 @@ func (s *Server) Shutdown(ctx context.Context) error {
 	// streams finish. The base request context remains live until the timeout
 	// path below, where connections are forcibly closed.
 	if shutdownConfig != nil && !alreadyClosing {
-		s.goAwaySent.Add(uint64(len(connections)))
+		s.goAwaySent.Add(uint64(protocolConnectionCount))
 		_ = shutdownConfig.Shutdown(context.Background())
 	}